Method of optical self-switching using microresonator optical switch having nanoparticles

ABSTRACT

An optical switch includes a microresonator comprising a plurality of silicon nanoparticles within a silicon-rich silicon oxide layer. The microresonator further includes an optical coupler optically coupled to the microresonator and configured to be optically coupled to a signal source. A method of optical switching includes providing an optical switch comprising an optical coupler and a microresonator having a plurality of nanoparticles and receiving an optical pulse by the optical switch, wherein at least a portion of the optical pulse is absorbed by the nanoparticles such that at least a portion of the microresonator undergoes an elevation of temperature and a corresponding refractive index change when the optical pulse has an optical power greater than a predetermined threshold level.

CLAIM OF PRIORITY

This application is a divisional of U.S. patent application Ser. No.13/453,588, filed Apr. 23, 2012 and incorporated in its entirety byreference herein, which is a divisional of U.S. patent application Ser.No. 12/699,578, filed Feb. 3, 2010 (now U.S. Pat. No. 8,184,932) andincorporated in its entirety by reference herein, which is a divisionalof U.S. patent application Ser. No. 11/522,802, filed Sep. 18, 2006 (nowU.S. Pat. No. 7,684,664) and incorporated in its entirety by referenceherein, and which claims the benefit of priority to U.S. ProvisionalPatent Appl. No. 60/717,637, filed Sep. 16, 2005, which is incorporatedin its entirety by reference herein.

U.S. GOVERNMENT LICENSE RIGHTS

This invention was made with U.S. Government support under contract0444731 awarded by the National Science Foundation. The U.S. Governmenthas certain rights in this invention.

BACKGROUND

1. Field

The present application relates generally to optical modulators andswitches.

2. Description of the Related Art

All-optical fiber modulators and switches are important devices thathave been researched for many years mainly because of the desire forlow-loss, low-power, fiber-interfaced, optically-addressable switchingdevices in optical communication and fiber sensor systems. These systemsinclude, but are not limited to, periodic self-healing communicationnetworks, re-configurable optical signal processing, packet switchingfor local area networks, bit switching, towed sensor arrays, and testingof fiber links.

Unfortunately, very few physical mechanisms are available to modulatethe refractive index of a silica fiber in order to induce switching. Thewidely-studied Kerr effect has an extremely fast response time (e.g., afew femtoseconds) but it is notoriously weak. Kerr-based fiber switchestypically utilize power on the order of 20 watts in a 10-meter fiber at1.55 micrometers for full switching (see, e.g., N. J. Halas, D. Krökel,and D. Grischkowsky, “Ultrafast light-controlled optical-fibermodulator,” Applied Physics Letters, Vol. 50, No. 14, pages 886-888,April 1987; and S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez,and P. S. Smith, “Femtosecond switching in a dual-core-fiber nonlinearcoupler,” Optics Letters, Vol. 13, No. 10, pages 904-906, October 1988)or a switching power-length product PL of approximately 200 watt-meters.Resonantly-enhanced nonlinearities in fibers doped with a rare earthsuch as Er³⁺ are considerably stronger (PL approximately equal to 10⁻²watt-meter) but are very slow (e.g., response time of approximately 10milliseconds; see, e.g., R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L.Chu, “Nonlinear refractive index in erbium doped optical fiber: theoryand experiment,” IEEE Journal of Quantum Electronics, Vol. 27, No. 4,pages 908-913, April 1991; and R. H. Pantell, R. W. Sadowski, M. J. F.Digonnet, and H. J. Shaw, “Laser-diode-pumped nonlinear switch inerbium-doped fiber,” Optics Letters, Vol. 17, No. 4, pages 1026-1028,July 1992). Switching has also been induced thermally in fibers dopedwith an absorber. For example, a 2.55-centimeter Co²⁺-doped fiber switchrequired a switching peak power of 1.8 kilowatts (PL approximately equalto 5 watt-meters), and its response time was approximately 25nanoseconds (see, e.g., M. K. Davis, and M. J. F. Digonnet, “Nanosecondthermal fiber switch using a Sagnac interferometer,” IEEE PhotonicsTechnology Letters, Vol. 11, No. 10, pages 1256-1258, October 1999).

More recently, Tapalian et al. (H. C. Tapalian, J.-P. Laine, and P. A.Lane, “Thermooptical switches using coated microsphere resonators,” IEEEPhotonics Technology Letters, Vol. 14, pages 1118-1120, August 2002)have demonstrated switching in a microsphere resonator coated with anabsorbing polymer by shining a 405-nanometer pump beam on themicrosphere's surface. The pump heated the polymer and the microsphere,which thermally shifted the microsphere's resonance wavelengths andswitched a 1.55-micrometer signal. The use of a resonator greatlyreduces the switching power: a pump exposure of only 4.9 milliwatts forapproximately 0.5 second was sufficient to shift the resonance byapproximately 1,000 linewidths. Since full switching requires a shift ofabout one linewidth, the switching power was only 4.9 microwatts, andthe switching energy of approximately 2.5 microjoules. However, theswitch response time was very long (e.g., 0.165 second). Taking thecharacteristic dimension of such a switch to be the sphere diameter (250micrometers in this case), this device has a PL product of approximately1.2×10⁻⁹ watt-meter, which is very low. Whispering gallery modemicrosphere resonators based on the Kerr effect have also beenpreviously studied (see, e.g., M. Haraguchi, M. Fukui, Y. Tamaki, and T.Okamoto, “Optical switching due to whispering gallery modes indielectric microspheres coated by a Kerr material,” Journal ofMicroscopy, Vol. 210, Part 3, pages 229-233, June 2003; A. Chiba, H.Fujiwara, J. Hotta, S. Takeuchi, and K. Sasaki, “Resonant frequencycontrol of a microspherical cavity by temperature adjustment,” JapaneseJournal of Applied Physics, Vol. 43, No. 9A, pages 6138-6141, 2004).Compared to other all-optical fiber switches, microsphere-based opticalswitches offer the unique advantages of extremely small size (e.g., amicrosphere is typically only 50-500 micrometers in diameter) and verylow switching energy. The reason is that the resonator has such sharpresonances that a very small change in the microsphere index issufficient to induce full switching.

SUMMARY

In certain embodiments, an optical switch comprises a microresonatorcomprising a plurality of nanoparticles. The microresonator isconfigured to receive signal light having a signal wavelength. At leasta portion of the microresonator is responsive to the signal light byundergoing a refractive index change at the signal wavelength.

In certain embodiments, an optical switch comprises a microresonatorcomprising a plurality of nanoparticles. The optical switch furthercomprises an optical coupler optically coupled to the microresonator.The optical coupler has a first portion configured to receive signalsfrom a signal source, a second portion optically coupled to the firstportion and configured to be optically coupled to the microresonator,and a third portion optically coupled to the second portion andconfigured to transmit signals received from the second portion. Theoptical switch transmits signals having a signal power greater than apredetermined threshold power from the first portion to the thirdportion and does not transmit signals having a signal power less thanthe predetermined threshold power from the first portion to the thirdportion.

In certain embodiments, a method fabricates an optical switch comprisinga microsphere coated with silicon nanocrystals. The method comprisesproviding a silica optical fiber. The method further comprises meltingat least a portion of the fiber to form at least one silica microsphere.The method further comprises coating the microsphere with a silicalayer. The method further comprises precipitating silicon nanocrystalswithin the silica layer by annealing the microsphere. The method furthercomprises passivating the nanocrystals by annealing the microsphere in ahydrogen-containing atmosphere.

In certain embodiments, a method of optical switching comprisesproviding an optical switch comprising an optical coupler and amicroresonator optically coupled to the optical coupler and having aplurality of nanoparticles. The method further comprises receiving anoptical pulse by the optical switch. At least a portion of the opticalpulse is absorbed by the nanoparticles of the microresonator such thatat least a portion of the microresonator undergoes an elevation oftemperature and a corresponding refractive index change when the opticalpulse has an optical power greater than a predetermined threshold level.

In certain embodiments, a method of optical switching comprisesproviding an optical switch comprising an optical coupler and amicroresonator optically coupled to the optical coupler and having aplurality of nanoparticles. The method further comprises receiving anoptical pulse by the optical switch. At least a portion of the opticalpulse is absorbed by the nanoparticles of the microresonator such thatat least a portion of the optical switch undergoes an increase of thenumber of free carriers therein and a corresponding refractive indexchange when the optical pulse has an optical power greater than apredetermined threshold level.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically illustrates an example optical switch compatiblewith certain embodiments described herein comprising a tapered fiberwith the pump pulse and the signal inputted to one end of the taperedfiber.

FIG. 2 schematically illustrates another example optical switchcompatible with certain embodiments described herein comprising atapered fiber with the pump pulse and signal inputted to opposite endsof the tapered fiber.

FIG. 3 schematically illustrates another example optical switchcompatible with certain embodiments described herein comprising a prismwhich couples the pump pulse and the signal to the microresonator.

FIG. 4 schematically illustrates another example optical switch forself-switching in accordance with certain embodiments described herein.

FIG. 5 is a flow diagram of an example method that fabricates an opticalswitch comprising a microsphere coated with silicon nanocrystals inaccordance with certain embodiments described herein.

FIG. 6 is a flow diagram of an example method for optical switching inaccordance with certain embodiments described herein.

FIG. 7 is a plot of measured transmission spectra of the output of anexample optical switch compatible with certain embodiments describedherein, with and without the pump pulse, showing a shift in theresonance wavelength shift when the pump is on at a peak-coupled powerof 3.4 microwatts.

FIG. 8 is a plot of the temporal response of the example optical switchof FIG. 3.

FIG. 9 is a diagram of an example pump pulse sequence and resultingswitched signal pulses in accordance with certain embodiments describedherein.

FIG. 10A is a diagram of three short pump pulses having the same peakpower but different widths, with each width being much shorter than τ₁.

FIG. 10B is a diagram of a resulting switched signal pulse correspondingto FIG. 10A for a resonance lineshape that is Lorentzian.

FIG. 10C is a diagram of a resulting switched signal pulse correspondingto FIG. 10A for a resonance lineshape that is Gaussian.

FIG. 10D is a diagram of a resulting switched signal pulse correspondingto FIG. 10A for a resonance lineshape that is rectangular.

FIG. 11 is a diagram of a pump pulse having a long width as compared tothe relaxation time of the mode volume (τ_(p)=50τ₁) and the resultingswitched signal pulse for a Lorentzian resonance lineshape.

FIG. 12A is a diagram of a pump pulse sequence with a high repetitionrate (T_(p)<<τ₂).

FIG. 12B is a diagram of the resulting sequence of switched signalpulses corresponding to FIG. 12A, with the dash-dotted curverepresenting the evolution of the mode volume baseline temperature.

FIGS. 13A and 13B schematically illustrate a side view and a top view,respectively, of one example optical switch comprising a microresonatorcompatible with certain embodiments described herein.

FIGS. 14A and 14B schematically illustrate a side view and a top view,respectively, of another example optical switch comprising amicroresonator compatible with certain embodiments described herein.

FIGS. 15A and 15B schematically illustrate a side view and a top view,respectively, of yet another example optical switch comprising amicroresonator compatible with certain embodiments described herein.

DETAILED DESCRIPTION

FIG. 1 schematically illustrates an optical switch 10 in accordance withcertain embodiments described herein. The optical switch 10 comprises amicroresonator 20 comprising a plurality of nanoparticles. Themicroresonator 20 is configured to receive signal light 30 having asignal wavelength and to receive a pump pulse 40 having a pumpwavelength. At least a portion of the microresonator 20 is responsive tothe pump pulse 40 by undergoing a refractive index change at the signalwavelength.

As schematically illustrated by FIG. 1, in certain embodiments, theoptical switch 10 further comprises an optical coupler 50 opticallycoupled to the microresonator 20 and configured to be optically coupledto a signal source 35 and to a pump source 45. The optical coupler 50transmits the pump pulse 40 from the pump source 45 to themicroresonator 20 and transmits the signal light 30 from the signalsource 35 to the microresonator 20.

In certain embodiments, the microresonator 20 comprises a microcavity, amicrosphere, a microring, a microdisc, a microtoroid, a waveguideresonator on a chip, or a high-Q microresonator (e.g., planarmicroresonator on a silicon chip). In certain embodiments, themicroresonator 20 comprises silica (SiO₂) glass, doped silica-basedglass (e.g., doped with germanium), borosilicate glass, ZBLAN glass,organic materials (e.g., polymethyl-methacrylate (PMMA)), or patternedoxynitride films on a silicon chip. The microresonator 20 can befabricated using various techniques and various standard semiconductormicrofabrication tools (see, e.g., D. K. Armani, T. J. Kippenberg, S. M.Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,”Nature, 27 Feb. 2003, Vol. 421, pages 925-928; F. Lissillour, D.Messager, G. Stéphan, and P. Féron, “Whispering-gallery mode laser at1.56 μm excited by a fiber laser,” Optics Letters, 15 Jul. 2001, Vol.26, No. 14, pages 1051-1053). Microring and microdisc resonators canalso be fabricated using various deposition techniques, including butnot limited to, chemical-vapor deposition (CVD) techniques employingSiH₄ and N₂O. Such on-chip resonators can also be coated with ananoparticle layer using CVD or other deposition techniques.

In certain embodiments, the microresonator 20 comprises a layer 22comprising the plurality of nanoparticles. The layer 22 can be at leasta portion of the outermost layer of the microresonator 20 or at least aportion of an inner layer of the microresonator 20 below an outersurface of the microresonator 20. As used herein, the term “layer” isused in its broadest ordinary meaning. For example, a layer may comprisea single material having a generally uniform thickness or may comprisemultiple sublayers each comprising a different material. In certainembodiments, the layer 22 comprises a first material (e.g., theplurality of nanoparticles) distributed either uniformly ornon-uniformly within a second material. In certain embodiments, thelayer 22 comprises two or more types of nanoparticles distributed eitheruniformly or non-uniformly within a second material. The layer 22 mayextend completely or substantially completely around the microresonator20, or it may extend only partly around the microresonator 20. The layer22 may be generally continuous or may comprise two or more expanses orregions that are non-contiguous with one another.

In certain embodiments, the nanoparticles are crystalline, while incertain other embodiments, the nanoparticles are amorphous. In certainembodiments, the nanoparticles comprise a semiconductor materialincluding but not limited to silicon, germanium, II-VI compoundsemiconductors (e.g., CdTe, CdS, or CdSe), III-V compound semiconductors(e.g., GaAs), or a metallic material with strong resonant absorption ina specific wavelength range due to surface plasmon resonance (e.g.,noble metals, Au, Ag, Cu, Al). Various types of microresonators 20discussed above can be easily coated with a layer of one or more ofthese types of nanoparticles. The nanoparticles of certain embodimentshave a strong absorption at the pump wavelength and a negligibleabsorption at the signal wavelength, as is described more fully below.

In certain embodiments described herein, a novel low-energy all-opticalfiber switch 10 comprises a silica microsphere resonator 20 coated withan silica layer 22 containing silicon nanocrystals. In certainembodiments, the switch 10 comprises a high-Q silica microsphere coatedwith a thin layer of silicon-rich silicon oxide (SRSO) in whichnanocrystals of silicon (Si) are precipitated, as described more fullybelow.

In certain embodiments, the signal source 35 comprises a tunable laserwhich generates signal light 30 having a signal wavelength (e.g., 1450nanometers) in the infrared portion of the electromagnetic spectrum. Incertain embodiments, the signal source 35 is a narrow-band tunablesource, while in certain other embodiments, the signal source 35 is awide-band tunable source. The signal wavelength of certain embodimentsis selected (i) to coincide with a whispering gallery mode or resonanceof the microresonator 20, and (ii) to be outside the absorption band ofthe nanoparticles so the signal is not significantly absorbed by thenanoparticles. For example, in certain embodiments in which themicroresonator 20 comprises a silica microsphere coated with a silicalayer 22 containing silicon nanoparticles, a signal wavelength of 1450nanometers is used since it is generally outside the absorption band ofsilicon. The signal wavelength of certain embodiments is in a rangebetween 500 nanometers and 2000 nanometers, in a range between 1300nanometers and 1600 nanometers, or in a range between 1300 nanometersand 1500 nanometers, while other signal wavelengths are also compatiblewith various embodiments described herein.

In certain embodiments, the pump source 45 comprises a laser 46 (e.g.,Argon-ion laser) which generates light having a pump wavelength (e.g.,488 nanometers) in the visible or infrared portions of theelectromagnetic spectrum. In certain embodiments, the laser 46 is anarrow-band tunable source, while in certain other embodiments, thelaser 46 is a wide-band tunable source. The pump source 45 of certainembodiments comprises a modulator 47 (e.g., mechanical chopper wheel,acoustic-optic modulator, or electro-optic modulator) which modulatesthe light from the laser 46 into short pulses of adjustable width at alow frequency (e.g., 10 Hz). Other types of modulators can be used tomodulate the pump into pulses of adequate width, such as directmodulation in the case of a semiconductor pump laser. In certainembodiments, the pump wavelength is shorter than the signal wavelength.In certain embodiments, the pump pulse 40 has a plurality of pumpwavelengths and the one or more pump wavelengths are selected to fallwithin the absorption band of the nanoparticles (e.g., siliconnanocrystals within a silicon-rich silicon oxide coating) such that thepump pulse 40 is significantly absorbed by the nanoparticles. Therefore,the pump pulse resonates poorly, if at all. The pump wavelength ofcertain embodiments is in a range between 300 nanometers and 1500nanometers, while other pump wavelengths (e.g., 820 nanometers, 980nanometers, 1060 nanometers, and 1480 nanometers) are also compatiblewith various embodiments described herein.

The optical coupler 50 transmits at least one pump pulse 40 from thepump source 45 to the microresonator 20 and transmits the signal light30 from the signal source 35 to the microresonator 20. As schematicallyillustrated in FIG. 1, the optical coupler 50 comprises an optical fiber52 (e.g., a single-mode fiber). In certain other embodiments, theoptical coupler 50 comprises an optical waveguide formed on a substrate(e.g., a semiconductor substrate such as a silicon wafer). In certainembodiments, the optical coupler 50 comprises one or more first portions53 configured to be optically coupled to the pump source 45 and to thesignal source 35, and a second portion 54 optically coupled to themicroresonator 20. The optical coupler 50 further comprises an outputportion 55 configured to be optically coupled to an optical system(e.g., comprising an optical detector 60 and an oscilloscope 70). Incertain embodiments, the first portion 53 and the third portion 55 ofthe optical coupler 50 are the same as one another.

In certain embodiments, the optical coupler 50 comprises a multiplexer56 (e.g., a wavelength-division multiplexer (WDM) fiber coupler), asschematically illustrated in FIG. 1, which multiplexes the signal 30 andthe pump pulse 40 into an input first portion 53 of a bi-taperedsingle-mode optical fiber 52 having a bi-tapered second portion 54optically coupled to the microresonator 20 and having an output portion55 optically coupled to an optical system (e.g., detector 60 andoscilloscope 70). The bi-tapered second portion 54 of the optical fiber52 in certain embodiments has a neck diameter of a few micrometers.

In certain other embodiments, the optical coupler 50 comprises twomultiplexers 56 (e.g., fiber, micro-, or bulk-optic) or two fibercirculators 57, as schematically illustrated in FIG. 2. In certain suchembodiments, the pump pulse 40 and the signal 30 are coupled todifferent first portions 53 (e.g., different ends of the optical fiber52) via a multiplexer 56 or a circulator 57 at each first portion 53, asschematically illustrated by FIG. 2, while in certain other suchembodiments, the pump pulse 40 and the signal 30 are coupled to the samefirst portion 53 (e.g., same end of the optical fiber 52) via themultiplexer 56, as schematically illustrated by FIG. 1. In certainembodiments, the optical coupler 50 advantageously minimizes signallosses by transmitting substantially all of the signal power to thetapered second portion 54. In certain embodiments, the optical coupler50 advantageously minimizes pump power losses by transmittingsubstantially all of the pump power to the tapered second portion 54. Incertain embodiments, the signal 30 is outputted to an optical system(e.g., comprising detector 60 a and oscilloscope 70 a) and the pumppulse 40 is monitored by the optical system (e.g., comprising an opticaldetector 60 b and an oscilloscope 70 b).

In certain embodiments, the optical coupler 50 comprises a prism 58, asschematically illustrated in FIG. 3. The prism 58 couples the pump pulse40 and the signal 30 to the microresonator 20 at different angles incertain embodiments in which the pump pulse 40 and the signal 30 havedifferent wavelengths. In certain embodiments, the pump pulse 40 and thesignal 30 are launched from opposite sides of the prism 58, asschematically illustrated in FIG. 3. Alternatively, the pump pulse 40and the signal 30 are launched from the same side of the prism 58 incertain other embodiments. In certain embodiments, the signal 30 isoutputted to an optical system (e.g., comprising detector 60 a andoscilloscope 70 a) and the pump pulse 40 is monitored by the opticalsystem (e.g., comprising an optical detector 60 b and an oscilloscope 70b).

In certain embodiments, at least a portion of the microresonator 20undergoes an increase in temperature and a corresponding change inrefractive index in response to the pump pulse 40. In certainembodiments, when a pump pulse 40 is launched into the microresonator20, the pump pulse 40 is absorbed by the nanoparticles, which heats themicroresonator 20 and changes its refractive index, and thus switchesthe signal 30 by shifting its resonance. For example, in certainembodiments in which the microresonator 20 comprises a microsphere witha silica layer containing silicon nanocrystals, the silica layerresponds to the pump pulse 40 by increasing in temperature such that themicroresonator 20 undergoes a corresponding refractive index change atthe signal wavelength. In certain embodiments, the microresonator 20 istransmissive to the signal 30 when the microresonator 20 is at theelevated temperature due to absorption of the pump pulse 40 and is nottransmissive to the signal 30 when the microresonator 20 is at a lowertemperature. In certain other embodiments, the microresonator 20 is nottransmissive to the signal 30 when the microresonator 20 is at theelevated temperature due to absorption of the pump pulse 40 and istransmissive to the signal 30 when the microresonator 20 is at a lowertemperature.

FIG. 4 schematically illustrates another example optical switch 10 inaccordance with certain embodiments described herein. The optical switch10 comprises a microresonator 20 comprising a plurality ofnanoparticles. In certain embodiments, the nanoparticles are in a layer22 of the microresonator 20. The optical switch 10 further comprises anoptical coupler 50 optically coupled to the microresonator 20. Theoptical coupler 50 has a first portion 53 configured to receive signals30 from a signal source 35, a second portion 54 optically coupled to thefirst portion 53 and configured to be optically coupled to themicroresonator 20, and a third portion 55 optically coupled to thesecond portion 54 and configured to transmit signals 30 received fromthe second portion 54 to an optical system (e.g., comprising an opticaldetector 60 and an oscilloscope 70). The optical switch 10 transmitssignals 30 having a signal power greater than a predetermined thresholdpower from the first portion 53 to the third portion 55. The opticalswitch 10 does not transmit signals 30 having a signal power less thanthe predetermined threshold power from the first portion 53 to the thirdportion 55.

In certain such embodiments, the optical switch 10 can be used as a“self-switch” which utilizes self-switching in the microresonator 20 inwhich the signal 30 switches itself and in which neither a multiplexernor a pump pulse is used. The signal 30 has a signal wavelength incertain such embodiments that coincides with one of the resonancewavelengths of the microresonator 20 (e.g., a whispering gallery mode).When the signal 30 has a low signal power and is launched into themicroresonator 20, the amount of signal power absorbed by themicroresonator 20 is sufficiently small that the temperature of themicroresonator 20 is essentially unchanged by the signal 30. Therefore,the low-power signal resonates within the microresonator 20 andessentially no power is transmitted to the third portion 55 of theoptical coupler 50.

When the signal power is increased, the amount of signal power absorbedby the microresonator 20 increases, and the signal power is dissipatedin the form of heat in the mode volume, thereby increasing thetemperature of the microresonator 20 and altering the resonancecondition by shifting the resonance wavelength of the microresonator 20.When the signal power is greater than a predetermined threshold power,the resonance wavelength of the microresonator 20 is shiftedsufficiently so that the high-power signal 30 does not resonate with themicroresonator 20 and a significant portion of the signal power istransmitted to the third portion 55 of the optical coupler 50. Thus, thehigh-power signal 30 has switched itself.

In certain embodiments, the optical switch 10 exhibits bi-stablebehavior. For example, for a continuous-wave (cw) signal 30 sent intothe input portion 53 of an optical coupler 50 coupled to amicroresonator 20, increasing the signal power correspondingly heats upthe microresonator 20, so that the signal 30 no longer resonates. Oncethe resonance wavelength has been shifted enough by the heat generatedby the signal power, the signal 30 no longer resonates with themicroresonator 20, so the signal 30 is transmitted to the output portion55 of the optical coupler 50, and the microresonator 20 cools down. Themicroresonator 20 then cools down until the resonant condition with thesignal 30 is reached and the signal 30 resonates again with themicroresonator 20, and the signal 30 is not transmitted to the outputportion 55 of the optical coupler 50, at which time the microresonator20 heats up again, etc. In certain embodiments, this bi-stable behavioris advantageously avoided by using signal pulses which are shorter thanthe thermal response time of the microresonator 20. For example, incertain embodiments, the signal source 35 comprises a laser 36 and amodulator 37 that determines the period of the signal pulses. In certainsuch embodiments, a signal pulse is received by the optical switch 10,heats up the microresonator 20, but is over by the time the heat has hadtime to flow out of the heated volume of the microresonator 20, so thesignal pulse does not experience the subsequent cooling of themicroresonator 20. Similarly, the next signal pulse advantageously isnot received by the optical switch 10 too soon after the previous signalpulse, since it is advantageous that the microresonator 20 be at ambienttemperature (e.g., not heated by the previous signal pulse) when thenext signal pulse arrives. In certain embodiments, the dynamics of thisoscillatory system advantageously permits fast switching processes(e.g., under the microsecond time scale).

Thus, in certain embodiments, whether the signal 30 is transmitted tothe third portion 55 of the optical coupler 50 or not is controlled bythe signal power level (e.g., for a low signal power, the signal outputis zero; for a high signal power, the signal output is maximum.) Such aself-switching embodiment can be used to sort out “zeros” and “ones” ina stream of data. In certain other embodiments, such a self-switch canbe used to regenerate signals. For example, for a signal pulse train ofzeros (low power pulses) and ones (high power pulses) being transmittedthrough an optical transmission line, noise in the transmission line'samplifiers can cause the zeros to no longer be true zeros, but to carrya little power. Sending this signal pulse train through a self-switchingoptical switch 10 can restore these small-power zeros to true zeros,since the zeros carry too little power to switch themselves, so theyresonate around the microresonator, where they lose all of their powerand thus are converted to true zeros.

FIG. 5 is a flow diagram of an example method 100 that fabricates anoptical switch 10 comprising a microsphere coated with siliconnanocrystals in accordance with certain embodiments described herein.The method 100 comprises providing a silica optical fiber (e.g., CorningSMF-28E optical fiber) in an operational block 110. The method 100further comprises melting at least a portion (e.g., one end) of thefiber to form at least one silica microsphere in an operational block120. In certain embodiments, microspheres with diameters ofapproximately 150 micrometers are fabricated by melting the tip of thesingle-mode silica fiber using approximately 3 watts of power from a125-watt 10.6-micrometer CO₂ laser and taking advantage of surfacetension to form spherical droplets with an atomically smooth surface(see, e.g., J.-Y. Sung, J. H. Shin, A. Tewary, and M. L. Brongersma,“Cavity Q measurements of silica microspheres with nanocrystal siliconactive layer,” in preparation). The typical Q factor of suchmicrospheres around 1450 nanometers was measured to be approximately5×10⁷.

The method 100 further comprises coating the microsphere with a silicalayer (e.g., 140 nanometers thick) in an operational block 130. Incertain embodiments, the microspheres are coated with a layer ofsilicon-rich silicon oxide (e.g., SiO_(x) with x<2) (SRSO) usinginductively-coupled plasma-enhanced chemical vapor deposition of SiH₄and O₂ with Ar plasma while rotating the microspheres to facilitate evencoating.

The method 100 further comprises precipitating silicon nanocrystalswithin the silica layer by annealing the microsphere in an operationalblock 140. The method 100 further comprises passivating the nanocrystalsby annealing the microsphere in a hydrogen-containing atmosphere in anoperational block 150. In certain embodiments, the microspheres areannealed first at 1100° C. for 60 minutes to precipitate the siliconnanocrystals, and then at 650° C. while in a forming gas for 60 minutesto hydrogen-passivate the dangling bonds in the nanocrystals. Thepresence of nanocrystals was confirmed in selected samples withtransmission electron microscopy (TEM). Reference samples were coatedwith silica instead of SRSO and underwent similar post-annealingtreatments. As expected, no nanocrystals were detected in thesereference samples. Because the signal (at approximately 1450 nanometers)falls out of the absorption band of Si nanocrystals, in certainembodiments, it is negligibly absorbed by the coating and the coatedmicrospheres still have a high Q at the signal wavelength (e.g.,approximately 3×10⁵ at 1450 nanometers).

In certain embodiments, the method 100 further comprises providing anoptical coupler 50 comprising an optical fiber 52 having a taperedportion 54 and optically coupling the tapered portion 54 to themicrosphere. In certain embodiments, the method 100 further comprisesoptically coupling a multiplexer 56 to the tapered optical fiber 52, themultiplexer 56 having a first portion configured to be optically coupledto a pump source 45, a second portion configured to be optically coupledto a signal source 35, and a third portion optically coupled to thetapered optical fiber 52. The multiplexer 56 is configured so that oneor more pump pulses 40 transmitted into the first portion of themultiplexer from the pump source 45 are transmitted to the taperedoptical fiber 52. The multiplexer 56 is further configured so that oneor more signals 30 from the signal source 35 are transmitted into thesecond portion of the multiplexer 56 to the tapered optical fiber 52.

FIG. 6 is a flow diagram of an example method 200 of optical switchingin accordance with certain embodiments described herein. The method 200comprises providing an optical switch comprising an optical coupler anda microresonator optically coupled to the optical coupler and having aplurality of nanoparticles, in an operational block 210. The method 200further comprises receiving an optical pulse by the optical switch in anoperational block 220. At least a portion of the optical pulse isabsorbed by the nanoparticles of the microresonator such that at least aportion of the microresonator undergoes an elevation of temperature anda corresponding refractive index change when the optical pulse has anoptical power greater than a predetermined threshold level.

In certain embodiments, the optical pulse is transmitted through theoptical switch when the optical power of the optical pulse is greaterthan the predetermined threshold level, and the optical pulse is nottransmitted through the optical switch when the optical power of theoptical pulse is less than the predetermined threshold level. In certainother embodiments, the optical pulse is not transmitted through theoptical switch when the optical power of the optical pulse is greaterthan the predetermined threshold level, and the optical pulse istransmitted through the optical switch when the optical power of theoptical pulse is less than the predetermined threshold level.

In certain embodiments, the method 200 further comprises receiving anoptical signal by the optical switch. In certain such embodiments, theoptical signal is transmitted through the optical switch when theoptical power of the optical pulse is greater than the predeterminedthreshold level, and the optical signal is not transmitted through theoptical switch when the optical power of the optical pulse is less thanthe predetermined threshold level. In certain other such embodiments,the optical signal is not transmitted through the optical switch whenthe optical power of the optical pulse is greater than the predeterminedthreshold level, and the optical signal is transmitted through theoptical switch when the optical power of the optical pulse is less thanthe predetermined threshold level.

In certain embodiments, the optical coupler comprises an optical fiberhaving a first portion, a second portion, and a tapered portion betweenthe first portion and the second portion and optically coupled to themicroresonator, and a multiplexer optically coupled to the opticalfiber. The method 200 further comprises sending the optical pulsethrough the multiplexer to the tapered portion of the optical fiber. Incertain embodiments, at least a portion of the optical pulse is absorbedby the microresonator such that the microresonator temperature iselevated. When an optical signal propagates through the tapered portionwhile the temperature of the microresonator is elevated, the opticalsignal propagates from the first portion to the second portion of theoptical fiber. When the optical signal propagates through the taperedportion while the temperature of the microresonator is not elevated, theoptical signal resonates with the microresonator and does not propagateto the second portion of the optical fiber. In certain embodiments, theoptical pulse and the optical signal are the same, such that the opticalpulse is self-switched. In certain embodiments, the microresonatorcomprises a silica microsphere coated with a silica layer containingsilicon nanocrystals.

Performance of Microsphere-Based Embodiments

In certain embodiments described herein, a novel low-energy all-opticalfiber switch 10 comprises a high-Q silica microsphere resonator 20coated with a thin layer of silicon-rich silicon oxide (SRSO) in whichnanocrystals of silicon (Si) are precipitated. Certain such embodimentsadvantageously use Si nanocrystals as an absorber instead of a polymer,as used by Tapalian et al., since (1) Si nanocrystals are compatiblewith standard micro-fabrication technologies, and (2) Si nanocrystalshave a broad absorption band that extends into the near infrared (IR),so that this switch 10 can advantageously be pumped with a standardlaser diode (e.g., at 808 nanometers). In certain embodiments, theoptical switch 10 uses a standard multiplexing scheme to couple the pumpand the signal into the microsphere through the same bi-tapered fiber.Certain such embodiments advantageously yield a more efficientutilization of the pump energy.

In certain embodiments, when a pump pulse is launched into themicrosphere, it is absorbed by the nanocrystal layer, which heats themicrosphere and changes its refractive index, and thus switches thesignal by shifting its resonance. A resonance wavelength shift of 5picometers, sufficient to fully switch the signal, was observed with apump pulse power of 3.4 microwatts and a pump pulse width of 25milliseconds, or a pump pulse energy of only 85 nanojoules. This resultis in good agreement with the prediction of a simple thermal model,described below. The rise time of the switch was measured to beapproximately 25 milliseconds (a value imposed by the pump peak power)and its fall time to be approximately 30 milliseconds (a value imposedby the microsphere's thermal time constant). This value is approximately5 times faster than previously reported (see, e.g., Tapalian et al.) andin agreement with predictions (see, e.g., V. S. Il'chenko and M. L.Gorodetskii, “Thermal nonlinear effects in optical whispering gallerymicroresonators,” Laser Physics, Vol. 2, pages 1004-1009, 1992). Theproduct of the switching peak power of 3.4 microwatts and the device'scharacteristic dimension (diameter of 150 micrometers) is 5.1×10⁻¹⁰watt-meter, which is one of the lowest values reported for anall-optical switch.

In the absence of the pump pulse, the signal is on resonance with themicrosphere, and the power of the signal is depleted, mostly byscattering, as the signal resonates around the microsphere. Thus, thesignal does not come out of the tapered fiber's output portion when themicrosphere is not excited by the pump pulse.

Upon being launched into the tapered optical fiber, the energy of thepump pulse is absorbed by the nanocrystals, which are thus excited abovetheir bandgap. As the nanocrystals relax to the ground state, heat isgenerated and transferred to at least a portion of the microsphere(e.g., the mode volume), which elevates the temperature of the heatedportion of the microsphere. This elevated temperature changes themicrosphere's refractive index and the dimensions of the microsphere.The absorption of the pump pulse by the microsphere causes its resonancewavelengths to shift. When the wavelength shift is large enough, thewavelength of the signal pulse no longer falls on the resonance to whichit was originally matched, and all the signal power comes out of theoutput portion of the tapered optical fiber. Thus, the signal has beenswitched.

After the pump pulse has passed through, the microsphere cools down toits initial temperature (e.g., through natural or forced convection intothe surrounding medium, typically air, although other fluids can beadvantageously used). The microsphere resonance wavelengths thus returnto their initial values, the signal pulses become resonant again withthe microsphere, and no signal power comes out of the output portion ofthe tapered optical fiber.

In certain embodiments, the nanocrystals increase the pump absorptionrate as compared to the pump scattering loss rate. Scattering in generaldoes not contribute to heating the microsphere, so by increasing thepump absorption rate as compared to the pump scattering loss rate, thepresence of nanocrystals increases the fraction of the pump energy whichis turned into heat. Thus, the nanocrystals advantageously reduce thepump energy required for switching. However, in certain embodiments inwhich the silica microsphere does not comprise silicon nanocrystals, thepump pulse is absorbed by the microsphere's silica material (which has alower ratio of absorption loss to scattering loss than do thenanocrystal-doped silica), and a higher switching power of the pumppulse is required.

The switching energy of certain embodiments can be evaluated with asimple thermal model. When the microsphere is heated, its refractiveindex changes through the index thermal coefficient ∂n/∂T of silica, andits diameter changes through thermal expansion of silica. Since theeffect of thermal expansion is about two orders of magnitude weaker thanthat of the index change, the thermal expansion can conveniently beneglected. The switching energy can therefore be obtained by calculatingthe index change which shifts the signal resonance by one linewidth(which is sufficient to fully switch the signal), then calculating theheat it takes to change the microsphere index by this amount. The changewith temperature in the resonance wavelengths of a microsphere around1450 nanometers, calculated from the microsphere's resonant conditionand the ∂n/∂T of silica (approximately 10⁻⁵° C.⁻¹) is approximately 10picometers/° C. For small temperature increases (e.g., δT<1° C.), byanalogy with an optical fiber (see, e.g., M. K. Davis, M. J. F.Digonnet, and R. H. Pantell, “Thermal effects in doped fibers,” Journalof Lightwave Technologies, Vol. 16, No. 6, pages 1013-1023, June 1998),the temperature of the microsphere at steady state (e.g., after the pumphas been on longer than the microsphere's relaxation time) is close touniform.

Energy conservation states that the heat that is to be injected into thesphere per unit time to maintain its steady-state temperature at atemperature δT above the temperature of the surrounding air is given by:{dot over (H)}=hAδT  (1)where h is the heat transfer coefficient of silica in air due to naturalconvection, and A is the microsphere area. If P_(abs) is the pump powerabsorbed by the microsphere, steady-state switching is achieved incertain embodiments when P_(abs)={dot over (H)}. In the example citedabove (85 nanojoules of switching energy), the microsphere has adiameter of 150 micrometers and a Q approximately equal to 3×10⁵. Theresonance linewidth around 1450 nanometers, and thus the wavelengthshift for full switching, is approximately 4.8 picometers, or atemperature change δT≈4.8/10=0.5° C. Assuming the h coefficient of thesilica microsphere to be the same as for a silica cylinder (h=81 W/m²/°C.), Equation 1 is used to show that the absorbed pump power forswitching is approximately 2.9 microwatts.

The degree of switching can be monitored experimentally in certainembodiments by continuously scanning the signal wavelength over theresonance to record the resonance dip on a digitizing oscilloscope. Thismeasurement can then be repeated with the pump laser on to record theshift in resonance at steady state.

In certain embodiments in which the taper is fairly lossy at the pumpwavelength, the taper loss at the pump wavelength is measured todetermine the pump power coupled into the microsphere. One method tomeasure the taper loss is to measure the pump power coupled into andexiting the tapered fiber when the microsphere is coupled to the taperedfiber, then to repeat this measurement when the microsphere is decoupledfrom the tapered fiber. This measurement is then repeated afterreversing the ports of the tapered fiber (i.e., when coupling the pumpat the output port). This set of measurements yields unambiguously thetransmission loss of the two tapered fiber sections (input to neck andneck to output) and the pump power absorbed in the microsphere. Asimilar measurement can be used for other microresonators (e.g.,toroidal microresonators).

FIG. 7 is a plot of the transmission spectrum of an example microsphereswitch measured with and without the pump to illustrate switching. Theresonance of FIG. 7 (with the pump either on or off) has afull-width-at-half-maximum (FWHM) of 4.8 picometers. Since the Q-factoris by definition related to the resonance linewidth Δλ by Δλ=λ_(s)/Q,where λ_(s) is the central signal wavelength, this measurement impliesthat the measured Q is approximately equal to (0.0048/1450), orapproximately 3×10⁵. The measured shift in resonance wavelength in FIG.7 is approximately 5 picometers for approximately 3.4 microwatts of pumppower absorbed by the microsphere. This shift is observed to increasewith increasing pump power. Thus, the resonance shift in FIG. 7 isapproximately equal to one linewidth of the signal, and is sufficient tofully switch between the “off” state and the “on” state of the opticalswitch.

This switching power agrees well with the value of 2.9 microwattspredicted earlier by theory. From this measured value and the length ofthe microsphere (150 micrometers), the calculated PL product of theexemplary switch is 5.1×10⁻¹⁰ watt-meter, or a factor of 3 lower thanthe values calculated from previously reported observations (see, e.g.,Tapalian et al.). In reference microspheres having silica coatings whichdid not contain Si nanocrystals, the shift induced by the pump pulse wasmeasured to be smaller than that shown in FIG. 7 by a factor ofapproximately 3.3. Thus, the pump power necessary to induce a wavelengthshift comparable to that of FIG. 7 using a microsphere without thenanocrystals is approximately a factor of 3.3 higher than the pump powerfor a microsphere with the nanocrystals. This result confirms that thenanocrystals of the example switch increase the pump absorption and thusreduce the switching energy requirement significantly.

FIG. 8 is a plot of the temporal response of the example switch of FIG.7. The temporal response was measured by tuning the signal to aresonance and adjusting the spacing between the tapered fiber and themicrosphere for critical coupling (e.g., zero transmitted signal power).The pump pulses were then turned on (150-millisecond width, 50% dutycycle, sub-millisecond rise and fall time) and the signal powertransmitted by the tapered fiber was recorded as a function of time.

In certain embodiments, longer pump pulses having lower peak power areused to excite the microsphere. The heat deposited by a relatively longpump pulse (e.g., on the order of 100 milliseconds) has time to migratethrough the entire microsphere before the end of the pump pulse, ratherthan remaining solely in the mode volume. As used herein, the term “modevolume” refers to the volume of the microresonator (e.g., microsphere)in which most (e.g., 95%) of the signal energy resonating with themicroresonator (e.g., whispering gallery mode) is located in themicroresonator. The amount of heat deposited in the microsphere by thepump pulse is then greater than if only the mode volume were heated,thus the switching energy is higher. After a pump pulse has traveledthrough the microsphere, it then takes considerably longer (e.g., by afactor of approximately 100, corresponding to the ratio of themicrosphere dimension to the mode dimension) for the larger amount ofheat to migrate out of the microsphere into the surrounding medium(e.g., air). Stated differently, the microsphere takes longer to cooldown, and therefore the fall time of the switch is correspondinglylonger than if the pump pulse had been shorter. Certain such embodimentsare advantageously used in applications in which the optical switch ismaintained in the “off” state for longer periods of time.

In certain embodiments, as schematically illustrated by FIG. 8, thefalling and rising edges of the switched pulse are approximatelyexponential, as expected from basic physics. Fitting an exponential tothe two edges gives a rise time constant of 25±5 milliseconds and a falltime constant of 30±5 milliseconds. The latter result agrees well withthe value calculated from V. S. Il'chenko et al. for the exemplarymicrosphere's dimensions. In certain other embodiments utilizing ashorter pump pulse, as described more fully below, the fall time isconsiderably shorter (e.g., a few microseconds). The fall time isdetermined at least in part by the time required for the microspheretemperature to reach equilibrium with the surrounding medium after thepump pulse has been turned off. In certain embodiments in which amicrotoroid is used instead of a microsphere, the fall time is fastersince the microtoroid has a smaller thermal mass than the microsphere(see, e.g., D. K. Armani, B. Min, A. Martin, K. J. Vahala, “Electricalthermo-optic tuning of ultrahigh-Q microtoroid resonators,” AppliedPhysics Letters, Vol. 85, No. 22, pages 5439-5441, November 2004).

The rise time of the optical switch is determined at least in part bythe rate at which heat is deposited into the microsphere (e.g., by thepump power for a fixed pump energy). In certain such embodiments, as thepump power is increased, the rise time increases. In certainembodiments, such as that of FIG. 8, it is purely coincidental that themeasured rise and fall time constants are comparable. From the measuredrise time and measured absorbed pump power for the device correspondingto FIGS. 7 and 8, the total energy required for full switching (namely,the energy for shifting the resonance wavelength by one linewidth) isestimated to be 3.4 microwatts multiplied by 25 milliseconds, orapproximately 85 nanojoules. This result is a factor of approximately 30lower than reported earlier (see, Tapalian et al.). In certain otherembodiments described more fully below, the switching energy is on theorder of a few hundred picojoules or lower.

Temporal Features of the Thermal Response

In certain embodiments, a microresonator (e.g., a microsphere or amicrotoroid) pumped optically by exciting a resonant whispering gallerymode heats up due to absorption of the pump photons in (or very near)the mode volume. The deposited heat raises the temperature of the modevolume, which changes the refractive index (and, to a lesser extent, thedimension of the microresonator), and thus changes all resonancewavelengths. As described above, this effect is used in certainembodiments to switch or modulate the amplitude of an optical signal offixed wavelength tuned to one of the resonances of the microresonator.When propagating through a nanowire (e.g., a tapered optical fiber)optically coupled to the microresonator when the pump is off, theoptical signal resonates with the microresonator, and only a smallfraction, if any, of the optical signal propagates out of an outputportion of the nanowire (e.g., zero transmission through the nanowire).When propagating through the nanowire when the pump is on, the opticalsignal is off resonance and a large fraction of the optical signal istransmitted through the output portion of the nanowire (e.g., 100%transmission through the nanowire). When the pump is modulated intopulses, the temperature of the mode volume increases and decreases eachtime a pump pulse is sent through, thereby alternatively turning thesignal on and off.

The temporal response of microcavities to thermal excitations cannot beneglected when considering the optical properties of these microcavities(see, e.g., T. Carmon, L. Yang, and K. J. Vahala, “Dynamical thermalbehavior and thermal self-stability of microcavities,” Optics Express,Vol. 12, No. 20, pages 4742-4750, October 2004). The temporal responseof the microresonator, and thus the temporal shape of the switchedsignal and its dependence on the width and spacing of the pump pulses,are qualitatively discussed below for certain embodiments in which themicroresonator comprises a microsphere. Similar behavior is exhibited bycertain other embodiments with other types of microresonators (e.g.,microtoroids).

As described by V. S. Il'chenko and M. L. Gorodetskii, cited previously,the temporal response of a microsphere is dictated by two thermal timeconstants: (i) the fast time constant τ₁ of the mode volume (of theorder of a few microseconds), and (ii) the slower time constant τ₂ ofthe entire microsphere (of the order of tens of milliseconds). If anextremely short pump pulse is launched into the mode volume, the modevolume heats up instantly, and while the pump pulse is on, the heatstored in the mode volume does not have time to diffuse out of the modevolume. After the pump pulse has passed through, the heat flows out ofthe mode volume. If the temperature rise is modest, this heat flowoccurs mostly into the microsphere via heat conduction, as well as intothe surrounding medium (e.g., air) via, for example, natural heatconvection. τ₁ is the time constant that characterizes how fast heatflows out, or equivalently how fast the temperature of the mode volumedrops, or how fast the switched signal returns to its unswitched (off)state. If the temperature drop exponentially, after a time t=τ₁, thesignal power is down from its switched power by 1/e, after 2τ₁ by 1/e²,etc. In certain embodiments, the switched signal is considered to beback to its unswitched state after 3τ₁-10τ₁, depending on the signalextinction ratio utilized in the application at hand.

Similarly, τ₂ characterizes the time it takes the heated microsphere (asopposed to the mode volume) to cool down (e.g., to room temperature T₀)after the source of heat has been turned off. In certain embodiments,the only heat loss mechanism is into the surrounding air via naturalconvection. Again, typically one can wait a few τ₂'s before the vastmajority of the heat stored in the microsphere has been drained and themicrosphere temperature is essentially back to room temperature.

To illustrate how the temporal shape of the sequence of switched signalpulses generated by such an optical switch depends on the duration andrepetition rate of the pump pulse relative to these two time constantsin various embodiments, the discussion below addresses three differentpump pulse sequences.

Short, Low-Repetition-Rate Pump Pulse Sequence

In certain embodiments, the pump pulse sequence has two characteristics:(1) each pump pulse has a duration τ_(p) short enough that the heatgenerated by the pump pulse does not have time to flow out of the modevolume while the pump pulse is on, and (2) a repetition rate(corresponding to a pulse-to-pulse spacing T_(p)) low enough that allthe heat generated by one pump pulse has time to drain out of themicrosphere (e.g., by natural convection) before the next pump pulsearrives. As illustrated in FIG. 7, each pump pulse injects adelta-function-like impulse of heat into the microsphere, the modevolume temperature increases sharply, the signal moves rapidly to itsswitched state, then quickly returns to its unswitched state after thepump pulse is off, and is fully in the unswitched state by the time thenext pump pulse arrives. This pump pulse sequence configuration producesthe shortest possible rise time and fall time for the switched signalpulses, albeit also a low repetition rate. Such a pump pulse sequenceconfiguration is used in certain embodiments to verify experimentallythe existence and value of the short time constant τ₁.

Characteristic (1) described above imposes that the pump pulse durationis shorter than τ₁. However, if the pump wavelength λ_(p) is tuned to aresonance and if the Q of the microsphere at λ_(p) is too high, the timeit will take the pump pulse to be completely absorbed may exceed τ₁, inwhich case this condition can just not be satisfied. As an example,consider a silica microsphere (refractive index n=1.44) with a diameterD=150 micrometers and a quality factor at the pump wavelength ofQ_(p)=10⁷. The time of flight of the pump pulse once around themicrosphere is t₀≈2.3 picoseconds, and the time it takes for all thepump energy of the pump pulse to be absorbed is of the order of themicrosphere time constant Q_(p)t₀≈23 microseconds. To be fullyresonating, and thus fully absorbed, the pump pulse advantageously has aduration of the same order as the microsphere time constant. Thus, if apump pulse of duration τ_(p)=23 microseconds is sent into themicrosphere, since τ_(p) is large compared to τ₁ (typically a fewmicroseconds), the heat generated by the pump pulse will start migratingout of the mode volume well before the pump pulse is off. In certainsuch embodiments, the switch is slow since it then takes much longer forthe switched signal to return to its unswitched state. In certainembodiments, Q_(p) is selected to be sufficiently low to avoid thiscondition. For example, if Q_(p) is only 10⁵, then the time for all thepump energy to be absorbed is reduced to approximately 0.23 microsecond.For a pump pulse of duration τ_(p)=0.23 microsecond, τ_(p) issufficiently small as compared to τ₁ so that the heat generated by thepump pulse advantageously remains in the mode volume while the pumppulse is on. In certain embodiments, the presence of Si nanoparticles onthe surface of the microsphere results in a low value of Q_(p) (e.g.,less than 10³, or less than 10), and characteristic (1) is satisfiedeven if extremely short pulses (as short as 2.3 picoseconds for a150-micrometer diameter sphere) are used.

Characteristic (2) described above imposes that the time T_(p) betweenconsecutive pump pulses be much larger than τ₂. A value of T_(p) of theorder of a few τ₂ or longer is adequate in practice to satisfycharacteristic (2).

Referring to FIG. 9, the rise time of the switched pulses depends in acomplicated way on the rate of absorption of the pump energy. As usedherein, E₁ refers to the pump energy that is deposited in the modevolume to shift the resonance wavelength of the signal by one half-widthat half resonance (HWHM) linewidth, defined above as Δλ. As used herein,this amount of energy is referred to as the switching energy E_(s). Notethat in other embodiments, fully switching the signal with a highextinction ratio might require that the resonance be shifted by morethan one linewidths (e.g., of the order of 3-10 linewidths, depending onthe lineshape and the desired degree of extinction). In certain suchembodiments, the energy required for switching the signal fully is ofthe order of 3E₁-10E₁. In the discussion below, full switching isassumed to require a shift of one linewidth (i.e., E_(s)=E₁).

For a given pump pulse energy E_(p) and duration τ_(p), the signal isfully switched when the absorbed pump energy reaches E_(s). If E_(p) issmaller than E_(s), then this condition for full switching is notreached, so that at the end of the pump pulse, the signal is onlypartially switched. The rise time t_(r) of the switched signal (definedas the time it takes the signal to be switched from its minimum orunswitched value to its maximum value) is then simply equal to τ_(p). IfE_(p) is larger than E_(s), then the signal will reach its fullyswitched state when the fraction E_(s) of the pulse energy is absorbed.The amount of time for the portion E_(s) of a pulse of energy E_(p) tobe absorbed by the mode volume depends on the value of τ_(p) compared tothe microsphere time constant Q_(p)t₀, where t₀ is the time of flight ofa pump photon once around the microsphere. If τ_(p)>Q_(p)t₀, then thepump pulse is resonating and the amount of time for absorbing the pulseis (E_(s)/E_(p))τ_(p). If τ_(p)<Q_(p)t₀, then the pump pulse does notlast long enough to be fully resonating, so it is not fully absorbed.Thus, unless the pump pulse is extremely short, when E_(p)≧E_(s) therise time of the switched pulse is t_(r)≈(E_(s)/E_(p))τ_(p).

In certain embodiments, E_(p) is chosen to be slightly larger thanE_(s). After t=t_(r), the remaining pump energy (E_(p)−E_(s)) continuesto be absorbed, the temperature of the mode volume continues to rise,and the resonance wavelength continues to shift. However, since thesignal is already fully switched, the additional shift that takes placeafter t_(r) has no effect on the switched signal, and the remaining pumpenergy is just wasted. Therefore, from an energy efficiency standpoint,for certain embodiments, it is best to select a pump energy equal to theswitching energy, E_(p)=E_(s). The rise time of the switched signalpulse is then t_(r)=τ_(p).

In certain embodiments, the pump pulse duration is shorter than τ₁ andis larger than Q_(p)t₀. For an example microsphere with D=150micrometers and a low Q_(p), Q_(p)t₀≈10 picoseconds and τ₁≈3microseconds, and τ_(p) is between approximately 10 picoseconds and afew microseconds. The rise time in certain such embodiments is of theorder of τ_(p).

In certain embodiments, the magnitude of the switched pulses iscontrolled by a combination of the energy (or peak power) and theduration of the pump pulse. FIG. 10A shows an example of three pumppulses with the same peak power but with three different widths, namelyτ_(p)/3, 2τ_(p)/3, and τ_(p), all much shorter than τ₁. The peak powerP_(p) is selected such that for the maximum of the three widths, thepulse energy E_(p)=P_(p)τ_(p) is equal to 3E₁.

In certain embodiments, the microresonator has a Lorentzian resonance:

$\begin{matrix}{{y(\lambda)} = {1 - \frac{1}{1 - \left( \frac{\lambda - \lambda_{0}}{\Delta\;\lambda} \right)^{2}}}} & (2)\end{matrix}$where λ₀ is the center wavelength of the unswitched signal. Thisdefinition corresponds to the description above in which Δλ is the HWHM.For the largest of the three widths (τ_(p)), by definition of E₁(E_(p)=3E₁) at the end of the pump pulse (time t=τ_(p)), the signalresonance has shifted by 3Δλ. Thus, using Equation (2), the signaltransmission at the peak of the switched state is y(λ)=1−1/(1+3²)=0.9,as shown in FIG. 10B. To increase the signal transmission to be closerto unity, certain embodiments either increase the pulse peak power orincrease the pulse duration. If the pump pulse width is reduced to2τ_(p)/3, then the switched pulse has the same rising edge except thatit ends at 2τ_(p)/3 instead of τ_(p). The shift in the resonancewavelength in such embodiments is only 2Δλ, so the maximum amplitude ofthe switched signal is reduced to 1−1/(1+2²)=0.8, as shown in FIG. 10B.Similarly, for the shortest of the three pump pulses (having a widthτ_(p)/3), the maximum switched signal amplitude is even lower, down to1−1/(1+1²)=0.5, as shown in FIG. 10B.

In certain embodiments, the shape of the resonance function affects theshape of the switched pulse's rising edge (e.g., the gradual leveling ofthe switched pulse as t increases from 0 to τ_(p)). If the resonance isGaussian instead of Lorentzian, the lineshape function is:

$\begin{matrix}{{y(\lambda)} = {1 - {\exp\left( {{- {\ln(2)}}\left( \frac{\lambda - \lambda_{0}}{\Delta\;\lambda} \right)^{2}} \right)}}} & (3)\end{matrix}$where the ln(2) factor ensures that y(λ) is consistent with thedefinition of Δλ as the HWHM width. For a pump pulse width of τ_(p), themaximum amplitude of the switched signal is given by Equation (3) to be1−exp(−ln(2)×3²)=0.998, as shown in FIG. 10C. This amplitude is muchcloser to unity than the amplitude obtained from a Lorentzian resonancewith the same pump pulse width, as shown in FIG. 10B, because a Gaussianhas shallower tails than a Lorentzian. As shown in FIG. 10C, theswitched signal is much more abrupt for a Gaussian resonance than for aLorentzian resonance.

As shown in FIG. 10D, for a resonance lineshape which is hypotheticallyrectanglular having a HWHM of Δλ, the switched signal reaches itsmaximum amplitude even more abruptly than for either a Gaussian or aLorentzian resonance. In fact, this maximum is reached when theresonance has shifted by only Δλ. Note that for a rectangular resonancelineshape, since the shift to achieve maximum amplitude is Δλ instead of3Δλ, the switching energy is reduced by a factor of three to E_(p)=E₁.

In certain embodiments, the fall time of the switched pulses is dictatedsolely by time it takes the heat to drain out of the mode volume byconvection. Thus, in certain such embodiments, the fall time is simplyequal to the thermal time constant τ₁. By measuring this fall time, thevalue of τ₁ can be directly obtained.

Long Pump Pulses with Low Repetition Rate

In certain embodiments, the pump pulses are much longer than τ₁ andspaced by a time T_(p) (approximately 200 milliseconds) much longer thanτ₂ (e.g., at most tens of milliseconds). T_(p) is now long enough thatthe microsphere has ample time between pump pulses to fully cool down toroom temperature. There is no net build-up of heat in the microsphereover time, so the discussion below focuses on the effects during asingle pump pulse.

In certain such embodiments, the start of the pump pulse is at time t=0,and from t=0 to t≈τ₁, heat accumulates in the mode volume and does nothave time to move very far out of it. Heat flows at a rate ofapproximately one mode volume characteristic width w (e.g., one or twomicrons for a typical microsphere) per τ₁, so between t=0 and t=τ₁, heatflows approximately w. However, up until the end of the pump pulse att=τ_(p), the heat generated in the mode volume has time to diffuse intothe bulk of the microsphere (e.g., at t=2τ₁, the heat has flowedapproximately 2w, at which time the heated volume is significantlylarger than the mode volume). Simultaneously with the diffusion of heatfrom the mode volume, more heat is injected into the mode volume, andthe temperature gradually climbs throughout the microsphere. As thetemperature of the microsphere rises, a second cooling mechanism becomesmore effective, namely natural convection into the air through thesurface of the microsphere. The higher the mean temperature of thesurface of the microsphere, the more dominant this second mechanismbecomes. For a given resonance lineshape, the shape of the switchedsignal depends again on the energy in the pump pulse.

As an example, consider a Lorentzian resonance and a pump pulse with awidth τ_(p)=50τ₁ and a peak power such that E_(p)=P_(p)τ_(p)=200E₁, asschematically illustrated by FIG. 11A. The start of the rising edge ofthe switched signal retains the same shape as in FIG. 10B up until timet≈τ₁. At t=τ₁ the amount of heat deposited in the mode volume is 4E₁, sothe resonance wavelength has shifted by 4Δλ. For the Lorentzianresonance lineshape, the signal is switched at 94%. As time goes onduring the pulse, the heat deposited by the pump pulse flows from themode volume towards the center of the microsphere and into thesurrounding air. The temperature of the mode volume continues to rise,but more slowly, so the resonance wavelength continues to shift awayfrom λ₀, but also more slowly. Note that the wavelength shift doescontinue indefinitely simply because the microsphere temperature cannotincrease indefinitely. As the surface temperature of the microsphereincreases, the quantity of heat flowing out of the surface per unit timedue to convection, which is proportional to the temperature differencebetween the surface and the air immediately surrounding it, alsoincreases. Once the surface temperature reaches the steady-state valueT_(ss) for which the outflow of heat per unit time due to convection isequal to the input of heat per unit time from the pump pulse, themicrosphere stops heating up.

In this exemplary embodiment, the only portion of the pulse energy thatis useful in inducing switching is approximately (τ₁/τ_(p))E_(p).Therefore, to switch the signal on and off as fast as possible incertain such embodiments, the pump pulse is advantageously turned offafter about τ₁. The rest of the pump pulse energy serves to maintain thesignal in the switched state, a feature that is useful in someapplications.

Note that in certain embodiments described above, the resonances of themicroresonator are assumed to be sufficiently far apart that when alarge resonance shift (e.g., a shift of the order of 200 linewidths) isinduced, the signal does not resonate with other resonances which havemoved to the signal wavelength such that the signal consequently remainsin the switched state. If this assumption does not apply, after asufficiently large shift (for example, a shift of more than a fewlinewidths), the signal wavelength will go through or reside near thenext resonance wavelength, and the signal power at the output of thetapered fiber will drop again. In certain embodiments, the opticalswitch can be designed using standard, well-known interferometryformulas to model the center wavelengths and widths of the resonances ofthe microresonator to determine a wavelength shift range that can betolerated by the optical switch. However, these center wavelengths andwidths are typically critical functions of generally non-measurablephysical details of the microresonator structure, including but notlimited to shape, dimensions, refractive index, and spatial distributionof the (often inhomogeneous) refractive index. Predicting theseparameters theoretically with the required precision to model theresonances of the microresonator can be very difficult. In such cases,it is simpler to access data regarding the resonances of themicroresonator through measurements using well-known and straightforwardtechniques.

A main difference between the embodiment illustrated by FIGS. 11A and11B and the embodiment illustrated by FIGS. 10A and 10B is that becausethe pump pulse of FIG. 11A is much longer than that of FIG. 10A, notjust the mode volume is heated by the end of the pump pulse, but alsothe microsphere. After the pump pulse (t>τ_(p)), it takes much longerfor this heat to drain out of the microsphere than for a short pumppulse (which only heats the mode volume). Therefore, the fall time ismuch longer, as illustrated in FIG. 11B. Quantitative estimation of thefall time can be made using a full-blown calculation of heat flow out ofthe microsphere. However, even without performing such a calculation, itis clear that the fall time is longest in embodiments in which the pumppulse width is equal to or longer than a few microsphere time constantsτ₂. In certain such embodiments, the microsphere reaches its maximumpossible temperature for this peak pump power since the stored heat ismaximized and the time for this heat to fully diffuse out of themicrosphere is also maximized. In certain such embodiments, the falltime then approaches τ₂, such that the fall time is between τ₁ and τ₂.In certain embodiments in which the pump pulse is on for approximately200 milliseconds (which is many times τ₂), the fall time is very closeto τ₂. This discussion explains the measured fall time of 30±5milliseconds described above, which is close to the value of τ₂predicted for this microsphere based on the theory of V. S. Il'chenkoand M. L. Gordetski, cited above.

FIG. 12A illustrates an example pump pulse sequence with apulse-to-pulse spacing T_(p) much smaller than τ₂. Unlike in theembodiments described above, because T_(p)<<τ₂, the microsphere in thisembodiment does not have sufficient time between pulses to fully cooldown to room temperature, and heat builds up in the microsphere overtime. As a result, the mean temperature of the microsphere risesgradually, and so does that of the mode volume, as shown qualitativelyby the dash-dotted curve in FIG. 12B. The jagged curve of FIG. 12Brepresents the instantaneous temperature rise of the mode volume. Aftersome time, of the order of a few τ₂'s, the surface temperature of themicrosphere reaches the steady-state value T_(ss) for which the heatflow out of the microsphere per pulse spacing T_(p) due to convectioninto air (or whatever other form of external coating is supplied, forexample, forced convection, conduction in a liquid, etc.) is equal tothe input of heat from each pump pulse. Under such conditions, themicrosphere stops heating, and its temperature levels off, as shown inFIG. 12B: the dash-dotted curve asymptotically approaches the dottedline, which represents the steady-state temperature of the microsphere'ssurface.

One feature of note shown by FIG. 12B is the shape of the individualsuccessive temperature spikes in the jagged curve. Careful examinationof FIG. 12B shows that this shape evolves from the start of the pumppulse train (t=0) to the time when the microsphere temperature reachesT_(ss). The heights and rise times are substantially constant for allthe temperature spikes, but the fall time gets shorter as thesteady-state is approached. In the first few pulses, the temperature ofthe microsphere is not very far above room temperature, and convectionplays a negligible role such that the microsphere and the mode volumeboth heat up fairly rapidly, shown by the high slope in the dash-dottedcurve of FIG. 12B. With increasing time, the temperature of the modevolume increases, the cooling due to convection gets more efficient,which means that the mode volume is able to cool down further betweenconsecutive pump pulses than it did at the start of the pump pulsesequence. Thus, the fall time of the successive temperature spikes inFIG. 12B gets shorter and shorter with each successive pump pulse.Eventually, the fall time is such that by the time the next pump pulsearrives, the temperature of the mode volume falls back to the value ithad at the start of the previous pump pulse. At this point, the systemhas reached thermal steady state such that the fall time remains at itssteady-state value and the temperature of the mode volume is the same atthe start of each pump pulse.

In certain embodiments, the plot of resonance wavelength versus time issubstantially identical to the instantaneous temperature curve of FIG.12B. The resonance wavelength shifts not only while a pump pulse is on,but also between pulses. Eventually, steady-state is reached, and witheach pump pulse, the signal wavelength shifts back and forth between thesame extreme values.

In certain embodiments, this temperature (and resonance wavelength)profile does not generally translate into a very useful switched signalpattern. If at time t=0 the signal is on resonance at wavelength λ₀, asthe baseline temperature of the mode volume increases, the meanresonance wavelength shifts from λ₀. If the mean temperature rise of themicrosphere is large enough, the resonance wavelength at steady-statewill be so far away from λ₀ that the signal will always be in theswitched state. In certain embodiments, this effect can of course beused to maintain a signal in the on state or the off state. It can alsobe used in certain embodiments to produce periodic switched signalpulses by tuning the signal wavelength to the resonance wavelength ofthe microsphere when the mode volume is at temperature T=T_(ss). Incertain such embodiments, the switch can be operated at a much higherrepetition rate (with smaller pulse spacing T_(p)) than possible if thesignal wavelength was tuned to a resonance of the microsphere at ambienttemperature T₀.

In certain embodiments, the optical switch is fiber pigtailed, so it isadvantageously easily interfaced with optical fiber components andoptical fiber systems. In certain embodiments, the optical switch isextremely small (e.g., having a microsphere of only 50-200 microns indiameter). In certain embodiments, the optical switch utilizes verylittle pump energy to be activated from an “off” state to an “on” state.The microresonator of certain embodiments has a high-Q at the signalwavelength (e.g., on the order of 10⁵ or higher), so the resonances areextremely sharp. One contribution to the sharpness of the resonance isthat only a small change in the refractive index is sufficient to shiftthe resonance away from the narrowband signal wavelength by one or moreresonance linewidths. Another contribution to the sharpness of theresonance is that the volume of silica in which the mode travels(namely, the mode volume) is very small, so only a small amount of heatis sufficient to change its temperature, and thus its refractive index.

In certain embodiments, the fall time of the switch is advantageouslyfast when the mode volume is sufficiently small (e.g., having atransverse dimension approximately equal to the wavelength of thesignal) so that only a small amount of time is taken for heat to diffuseout of the mode volume, once the pump pulse is gone. The rise time ofcertain embodiments is reduced by reducing the rise time of the pumppulse (e.g., under a nanosecond), and the fall time is only a fewmicroseconds. In certain embodiments, the microsphere is actively cooled(e.g., by forcing cooling air across the surface of the microsphere) toshorten the fall time. In certain embodiments, the switching power isextremely low (e.g., on the order of 100 nanowatts or less). Thus, theswitching energy of certain embodiments is on the order of 10⁻¹³ joules.

Reducing Fall Time and/or Switching Energy

Various approaches are compatible with certain embodiments describedherein to reduce the fall time of the microresonator switch when theswitch is pumped with pulses sufficiently long such that a substantialportion of the microresonator volume is heated by the end of the pulse.Some of these approaches rely on modifying the shape of a microresonator(e.g., microsphere) in order to reduce its volume and thus reduce thevolume that is heated, and thereby reduce the fall time of themicroresonator. In certain embodiments, this modification has theimportant additional benefit of reducing the amount of pump power thatis needed for switching the optical signal.

In certain embodiments, the mass of the microresonator is advantageouslyreduced, thereby reducing the time for the microresonator to cool downand the fall time of the optical switch. In certain such embodiments,the microresonator comprises a microsphere from which at least oneportion of the microsphere, away from the mode volume, (e.g., the core)has been removed. Depending on the microresonator material and the sizeand shape of the removed portion, the removal can be performed using avariety of conventional techniques, including but not limited to,reactive ion etching, chemical etching, and laser ablation.

FIGS. 13A and 13B schematically illustrate a side view and a top view,respectively, of one example configuration of an optical switch 300comprising a bi-tapered optical fiber 310 and a microresonator 320optically coupled to the optical fiber 310 in accordance with certainembodiments described herein. The configuration shown in FIGS. 13A and13B comprises a hole 330 formed (e.g., etched or drilled) through thetop portion of the microsphere 320, where the top 350 is defined as theend of the microsphere 320 opposite from the fiber post 360 to which itis attached. The hole 330 does not go all the way through themicrosphere 320 but stops some depth into the microsphere 320. The depthand diameter of the hole 330 determine the volume of removed material,which determines the switch's fall time and switching energy. Since thedepth of the hole 330 affects the mechanical strength of the microsphere320, this depth is advantageously chosen so as not to compromise themicrosphere's structural integrity. The hole 330 can be fabricated by anumber of standard techniques, including but not limited to reactive ionetching, chemical etching combined with conventional masking techniques,mechanical drilling, etc. The hole 330 can have any other shape that isconvenient to fabricate, or any shape that allows substantially the samevolume removal while providing superior mechanical strength (e.g., aconical hole). In certain embodiments, more than one hole 330 can bedrilled into the microsphere 320, at different locations, with differentorientations and shapes. In certain such embodiments, the holes 330advantageously do not get too close (within a few signal wavelengths) ofthe mode volume so that neither the signal nor the pump loss areincreased by the presence of the holes 330.

FIGS. 14A and 14B schematically illustrate another example configurationof an optical switch 400 comprising a bi-tapered optical fiber 410 and amicroresonator 420 optically coupled to the optical fiber 410 inaccordance with certain embodiments described herein. The configurationshown in FIGS. 14A and 14B comprises removing the top of the microsphere420, thereby producing a truncated or flat-topped microsphere 420. Themicroresonator 420 of FIGS. 14A and 14B can be fabricated by the sametechniques as described above with regard to the microresonator of FIGS.13A and 13B, as well as grinding and optionally polishing. In certainembodiments, the width of the top 450 is not so wide as to affect theloss of the pump and signal. Thus, in certain such embodiments, the flattop 450 is not closer than about a few wavelengths of the edges of themode volume. The width of the top 450 determines the fall time andswitching energy of the switch. In certain other embodiments, the top450 is not flat (e.g., curved). In certain embodiments in which the top450 is close to the equator of the microsphere 420, as in FIGS. 14A and14B, essentially half of the microsphere volume has been removed. Thus,in certain such embodiments, the fall time and the switching energy haveboth been reduced by approximately a factor of two. In certainembodiments, the reduction of the fall time and the switching energy arealso affected by the presence of the fiber post 460, which drains heatfrom the microsphere 420, thereby reducing the fall time but increasingthe switching energy.

In certain embodiments, the switching energy of the microresonator isreduced by fabricating the microresonator from a microsphere formed froma smaller diameter fiber, and/or reducing the diameter of the post thatholds the fiber, for example by chemical etching. Certain suchembodiments advantageously reduce the amount of lost heat that flows outof the microsphere while it is pumped. By the same token, certain suchembodiments advantageously increase the fall time of the switch, sincenow one of the paths through which heats migrates out of the microsphereduring cooling has been made less efficient. The choice of the diameterof the post involves making a compromise between the fall time and theswitching energy.

FIGS. 15A and 15B schematically illustrate a side view and a top view,respectively, of yet another example optical switch 500 comprising abi-tapered optical fiber 510 and a microresonator 520 optically coupledto the optical fiber 510 in accordance with certain embodimentsdescribed herein. In certain embodiments, as schematically illustratedby FIGS. 15A and 15B, the post is completely removed, for example bygrinding or chemical etching, and the microresonator is held onto asupport by other mechanical means that minimize the contact surface(e.g., bonding). In certain such embodiments, the bonding substratecomprises a good thermal insulator (such as a polymer), thereby loweringthe switching energy (at the cost of a slower fall time). In certainother embodiments, the bonding substrate comprises a good thermalconductor (such as a metal), thereby shortening the fall time (at theexpense of a higher switching energy). After removal of the post, thebottom (post-side) of the microresonator 520 can be removed, asdescribed above in relation to removing the top, thereby leaving a thindisk that can be again bonded either to a substrate or to a substratevia a small-diameter post. In certain such embodiments, as schematicallyillustrated in FIGS. 15A and 15B, the microresonator 520 resembles amicrotoroid, in which most of the original microsphere material has beenremoved. In certain embodiments, both the fall time and the switchingenergy have been dramatically reduced, e.g., by a factor of 10 to 100 orgreater, depending on the thickness of the disk. In certain embodiments,the disk can be in intimate contact (e.g., bonded) with a thermalconductor to further reduce the fall time, at the expense of theswitching energy.

In certain embodiments, both the switching energy and the fall time arereduced by using a smaller diameter microsphere as the microresonator.The fall time is roughly proportional to volume of the microsphere, asdescribed in V. S. Il'chenko and M. L. Gorodetskii, previously cited.Similarly, the switching energy is roughly proportional to volume of themicrosphere. For example, using a microsphere with a diameter, of 50micrometers instead of 150 micrometers, the fall time drops roughly fromabout 30 milliseconds to about 3.3 milliseconds, and the switchingenergy drops from about 85 nanojoules to less than about 10 nanojoules.

Free-Carrier-Induced Switching Mechanism

In certain embodiments, a method of optical switching comprisesproviding an optical switch comprising an optical coupler and amicroresonator optically coupled to the optical coupler and having aplurality of nanoparticles. The method further comprises receiving anoptical pulse by the optical switch, wherein at least a portion of theoptical pulse is absorbed by the nanoparticles of the microresonatorsuch that at least a portion of the optical switch undergoes an increaseof the number of free carriers therein and a corresponding refractiveindex change when the optical pulse has an optical power greater than apredetermined threshold level.

As described above, in certain embodiments, the microresonator has anoptical resonance which shifts in frequency or wavelength with regard toan optical signal due to a thermally-induced refractive index change. Incertain other embodiments, the refractive index of the microresonator ismodified by the generation of free carriers in the nanoparticles. Anempirical relationship, described by R. Soref and B. R. Bennet,“Electrooptical Effects in Silicon,” IEEE J. Quantum Electron., QE-23,pp. 123-129 (1987), quantifies observed changes in the refractive index(Δn) and the attenuation coefficient (Δα) due to free carriers in bulkSi near 1.5 microns.Δn=−(8.8×10⁻²² n+8.5×10⁻¹⁸ p ^(0.8))  (4)Δα=8.5×10⁻¹⁸ n+6.0×10⁻¹⁸ p  (5)Relatively moderate free carrier concentrations can significantly shiftthe resonance. Thus, in certain embodiments, optical switching can beobtained by the free-carrier-induced absorption, for which silicon andother semiconductor nanoparticles are well suited.

As an example embodiment with a Si-nanoparticle-doped microsphere, theSi nanoparticles have typical absorption cross sections at the pumpwavelength λ of 488 nanometers (corresponding to a frequency υ=6.1×10¹⁴Hz) of σ_(A)=10⁻¹⁶ cm² (10⁻²⁰ m²). Typical nanocrystal densities thatcan be obtained are about N_(Si)=10¹⁹ cm⁻³ (10²⁵ m⁻³) and thefluorescence lifetime is about τ=10 microseconds. (See, e.g., F. Prioloet al., Mat. Sci. Eng. B, Vol. 81, p. 9 (2001).) The absorption depth isthus expected to be small (e.g., d_(1/e)=N_(Si)σ_(A)=10 microns) and noresonant enhancement of the pump is expected.

Using a simple quasi-two-level rate equation model, the number ofexcited electron-hole pairs, N_(Ex), follows from:

$\begin{matrix}{\frac{\mathbb{d}N_{Ex}}{\mathbb{d}t} = {{N_{0}R} - \frac{N_{Ex}}{\tau}}} & (5)\end{matrix}$Where N₀(N_(Si)−N_(Ex)) is the number of Si nanoparticles in the groundstate and R is the pump up rate for the nanoparticles. This rate can becalculated from:

$\begin{matrix}{R = {{\phi\;\sigma_{A}} = \frac{P\;\sigma_{A}}{A_{Mod}h\;\upsilon}}} & (6)\end{matrix}$Where φ is the photon flux, which equals the used power, P=3.4 μW,divided by the mode area, A_(Mod) (about a λ²≈0.5 μm²=0.25×10⁻¹² m²),and the photon energy, hσ.

Solving for the excited concentration of electron-hole pairs gives:

$\begin{matrix}{N_{Ex} = {{N_{Si}\frac{\tau\; R}{{\tau\; R} + 1}} = {{N_{Si}\frac{\tau\;\phi\;\sigma_{A}}{{\tau\;\phi\;\sigma_{A}} + 1}} = {{N_{Si}\frac{\tau\;\sigma_{A}{P/A_{Mod}}h\;\upsilon}{{\tau\;\sigma_{A}{P/A_{Mod}}h\;\upsilon} + 1}} = {0.97 \times 10^{18}\mspace{20mu}{cm}^{- 3}}}}}} & (7)\end{matrix}$Where n and p are the electron and hole concentration in units of cm⁻³.For the carrier concentrations mentioned above:Δn=−(8.8×10⁻²²×[0.97×10¹⁸]+8.5×10⁻¹⁸×[0.97×10¹⁸]^(0.8)=8.5×10⁻⁴  (8)Δα=8.5×10⁻¹⁸×[0.97×10¹⁸]+6.0×10⁻¹⁸×[0.97×10¹⁸]=66 cm⁻¹  (9)

In certain embodiments, the refractive index change Δn is two orders ofmagnitude larger than the index change from thermal effects. Theattenuation coefficient change Δα can be converted into a Q value using:

$\begin{matrix}{Q = {{\frac{\pi\; n_{{SiO}_{2}}}{\lambda_{s}\Delta\;\alpha} \approx \frac{\pi \times 1.5}{1.5 \times 10^{- 4} \times 66}} = 476.}} & (10)\end{matrix}$This result implies that the presence of the free carriers would reducethe Q from 3×10⁵ to 476 and also be capable of switching the signal.

Different semiconductor nanoparticles will have different cross sectionsfor absorption and different excited carrier lifetimes. For example,direct bandgap semiconductor nanoparticles can be used to make fasterswitches. In certain embodiments, both the thermal mechanism and thefree-carrier mechanism contribute to the refractive index changeresulting from the interaction of the pump pulse with the nanoparticlesof the microresonator.

Various embodiments of the present invention have been described above.Although this invention has been described with reference to thesespecific embodiments, the descriptions are intended to be illustrativeof the invention and are not intended to be limiting. Variousmodifications and applications may occur to those skilled in the artwithout departing from the true spirit and scope of the invention asdefined in the appended claims.

What is claimed is:
 1. A method of optical switching, the methodcomprising: providing an optical switch comprising an optical couplerand a microresonator optically coupled to the optical coupler and havinga plurality of nanoparticles; and receiving an optical pulse by theoptical switch, wherein at least a portion of the optical pulse istransmitted through the optical coupler and is absorbed by thenanoparticles of the microresonator such that at least a portion of themicroresonator undergoes an elevation of temperature and a correspondingrefractive index change when the optical pulse has an optical powergreater than a predetermined threshold level, wherein transmission ofthe optical pulse through the optical switch is dependent on arelationship between the optical power of the optical pulse and thepredetermined threshold level.
 2. The method of claim 1, wherein theoptical pulse is transmitted through the optical switch when the opticalpower of the optical pulse is greater than the predetermined thresholdlevel and the optical pulse is not transmitted through the opticalswitch when the optical power of the optical pulse is less than thepredetermined threshold level.
 3. The method of claim 1, wherein theoptical pulse is not transmitted through the optical switch when theoptical power of the optical pulse is greater than the predeterminedthreshold level and the optical pulse is transmitted through the opticalswitch when the optical power of the optical pulse is less than thepredetermined threshold level.
 4. The method of claim 1, wherein theoptical pulse has a duration such that heat generated by the opticalpulse within a mode volume of the microresonator does not flow out ofthe mode volume during the duration of the optical pulse.
 5. The methodof claim 1, wherein the optical pulse has a duration such that heatgenerated by the optical pulse within a mode volume of themicroresonator flows out of the mode volume during the duration of theoptical pulse.
 6. The method of claim 1, wherein the plurality ofnanoparticles comprises silicon nanocrystals within a silica layer ofthe microresonator.
 7. The method of claim 6, wherein the plurality ofnanoparticles are passivated by hydrogen.
 8. The method of claim 6,wherein the silica layer comprises silicon-rich silicon oxide.
 9. Themethod of claim 1, wherein the optical coupler comprises an opticalfiber having a tapered portion optically coupled to the microresonator.10. A method of optical self-switching, the method comprising: providingan optical switch comprising an optical coupler and a microresonatoroptically coupled to the optical coupler and having a plurality ofnanoparticles; and receiving an optical signal by the optical switch,the optical signal having a signal wavelength, at least a portion of theoptical signal is transmitted through the optical coupler and isabsorbed by the nanoparticles of the microresonator such that at least aportion of the microresonator undergoes an elevation of temperature anda corresponding refractive index change when the optical signal has anoptical power greater than a predetermined threshold level, whereintransmission of the optical signal through the optical switch isdependent on a relationship between the optical power of the opticalsignal and the predetermined threshold level.
 11. The method of claim10, wherein the signal wavelength coincides with a resonance wavelengthof the microresonator.
 12. The method of claim 10, wherein the opticalsignal is transmitted through the optical switch when the optical powerof the optical signal is greater than the predetermined threshold leveland the optical signal is not transmitted through the optical switchwhen the optical power of the optical signal is less than thepredetermined threshold level.
 13. The method of claim 10, wherein theoptical signal is not transmitted through the optical switch when theoptical power of the optical signal is greater than the predeterminedthreshold level and the optical signal is transmitted through theoptical switch when the optical power of the optical signal is less thanthe predetermined threshold level.
 14. The method of claim 10, whereinthe optical signal has a duration shorter than a thermal response timeof the microresonator.
 15. The method of claim 14, wherein heatgenerated by the optical signal within a mode volume of themicroresonator does not flow out of the mode volume during the durationof the optical signal.
 16. The method of claim 10, further comprisingreceiving a second optical signal by the optical switch after receivingthe optical signal and after the microresonator has returned to anambient temperature.
 17. The method of claim 16, wherein a signal pulsetrain comprises the optical signal and the second optical signal, themethod further comprising regenerating the signal pulse train.